The magnetohydrodynamic equilibrium of a helical-axis heliotron with large-vacuum magnetic islands is investigated. Since the helical-axis heliotron is an $L\,{=}\,1/M\,{=}\,4$ low-magnetic-shear configuration, there is the sensitivity to the perturbed field. By assuming the external trim coil, low-order magnetic islands with $n/m\,{=}\,$1/2 can be generated. The effect and change of low-order ($n/m\,{=}\,1/2$) vacuum islands to the finite $\beta$ equilibrium are investigated. For a finite β equilibrium, $n/m\,{=}\,$1/2 islands disappear but $n/m\,{=}\, 4/8$ islands appear by the pressure-induced field. For another case, $n/m\,{=}\,$1/2 islands disappear and other resonances are suppressed. This property depends on the phase of islands.